{ "embedding_params": { "feature_scale": 1.0, "packing_ratio": 6.0, "separation_ratio": 6.0, "target_packing_distance": 6.0, "hard_min_clearance_ratio": 0.2, "hard_min_clearance": 0.2, "target_min_separation": 0.2, "preferred_min_separation": 0.95, "preferred_min_separation_ratio": 0.95, "noise_ratio": 0.04285250616657629, "sampling_density_per_feature": 24.593173564220816, "edge_length_jitter_ratio": 0.11846984323102307, "branch_angle_spread": 0.7279413083401358 }, "embedding_dimension": 2, "requested_embedding_dimension": 2, "feature_thickness_ratio": 0.782242435794394, "feature_thickness_budget": 0.782242435794394, "tube_sampling_mode": "solid", "num_components": 1, "component_gap_ratio": 7.389681813130521, "component_node_ids": [ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ], "component_x_intervals": [ [ 0.0, 3.607521670897329 ] ], "component_topology_classes": [ "single_cycle" ], "crowding_r": 0.06799159982269508, "crowding_gamma": 0.9392617227990151, "crowding_gamma_min": 0.10667968750000001, "crowding_admissibility_epsilon_sep": 0.27478949151880594, "thickness_aware_min_required_clearance": 0.02, "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding", "cycle_tree_edges": [], "cycle_lengths": { "0": 6 }, "pair_separations": {}, "cycle_nodes": { "0": [ 0, 1, 2, 3, 4, 5 ] }, "cycle_motifs": { "0": { "cycle_id": 0, "original_cycle_length": 6, "original_motif_vertices": [ 0, 1, 2, 3, 4, 5 ], "final_nodes": [ 0, 1, 2, 3, 4, 5 ] } }, "attachments": [], "edge_cycle_membership": { "(0, 1)": [ 0 ], "(1, 2)": [ 0 ], "(2, 3)": [ 0 ], "(3, 4)": [ 0 ], "(4, 5)": [ 0 ], "(0, 5)": [ 0 ] }, "num_cycles_ground_truth": 1, "betti_1": 1, "leaf_count": 2, "branch_nodes": [ 2 ], "is_planar": true, "max_edge_cycle_multiplicity": 1, "branch_params": { "num_initial_attachment_sites": 1, "max_branch_depth": 1, "promotion_prob": 0.422815246831306, "children_per_branch_point_range": [ 1, 3 ], "branch_length_range": [ 1, 4 ], "max_degree": 4, "max_total_nodes": 80, "max_total_edges": 88 }, "branch_attachment_nodes_initial": [ 2 ], "branch_generation_nodes": { "1": [ 6, 7, 8, 9 ] }, "branch_parent_map": { "6": 2, "7": 6, "8": 2, "9": 8 }, "branch_root_map": { "6": 2, "7": 2, "8": 2, "9": 2 }, "branch_depth_map": { "6": 1, "7": 1, "8": 1, "9": 1 }, "num_leaves_after_branching": 2, "num_branch_nodes_after_branching": 1, "betti_1_after_branching": 1, "embedding_valid": true, "embedding_dimensions_attempted": [ 2 ], "embedding_attempt_history": [ { "dimension": 2, "embedding_valid": true, "global_embedding_attempts": 1, "local_placement_rejections": 0, "min_nonadjacent_node_distance": 2.5149595929643613, "min_nonincident_edge_distance": Infinity, "min_nonincident_node_edge_distance": 2.677090133965939, "failure_reason": null, "refinement_applied": true, "refinement_iterations": 24, "refinement_objective_delta": -0.06883887723938287, "refinement_clearance_delta": 0.042645015481136195 } ], "embedding_constructive_success": true, "embedding_rejected": false, "min_nonadjacent_node_distance": 2.5149595929643613, "min_nonincident_edge_distance": Infinity, "min_nonincident_node_edge_distance": 2.677090133965939, "global_embedding_attempts": 1, "total_global_embedding_attempts": 1, "local_placement_rejections": 0, "embedding_fallback_used": false, "embedding_fallback_mode": null, "embedding_refinement": { "enabled": true, "applied": true, "iterations": 24, "objective_before": 0.7209881698057169, "objective_after": 0.652149292566334, "objective_delta": -0.06883887723938287, "clearance_before": 2.472314577483225, "clearance_after": 2.5149595929643613, "clearance_delta": 0.042645015481136195, "accepted_steps": 24, "reason": "accepted" }, "topology_class": "single_cycle", "sampled_topology_spec": { "topology_class": "single_cycle", "children_per_branch_point_range": [ 1, 3 ], "branch_length_range": [ 1, 4 ], "max_branch_depth_range": [ 1, 1 ], "promotion_prob_range": [ 0.2, 0.6 ], "max_degree": 4, "num_cycles": 1, "branch_attach_count": 1 }, "tube_embedding_separation_ratio": 6.0, "realized_post_crowding_min_nonadjacent_node_distance": 2.3623368414171972, "realized_post_crowding_min_nonincident_edge_distance": Infinity, "realized_post_crowding_min_nonincident_node_edge_distance": 2.6676304893134075, "realized_post_crowding_min_structural_distance": 2.3623368414171972, "realized_post_crowding_separation_to_feature_scale": 2.3623368414171972, "realized_post_crowding_separation_to_post_median_edge": 2.515542234710871, "realized_post_crowding_absolute_hardness": 0.42330965782173835, "minimum_realized_component_gap": Infinity, "feature_thickness_radius": 0.12739474575940296, "effective_max_tube_radius_for_sampling": 0.16285839265422775, "cycle_hole_radius_cap": 0.16285839265422775, "cycle_hole_radius_fraction": 0.2, "crowding_applied": true, "crowding_isotropy_epsilon": 0.05, "crowding_axis": [ -0.995481723833892, 0.09495334387320357 ], "crowding_centroid": [ 1.8172572040531105, 0.08596980826040913 ], "crowding_covariance_eigenvalues": [ 1.3978764647083721, 0.6689010138620367 ], "crowding_covariance_matrix": [ [ 1.391303921800157, -0.06890590765270181 ], [ -0.06890590765270181, 0.6754735567702518 ] ], "crowding_isotropic_fallback_used": false, "crowding_linear_operator": [ [ 0.9994523753404713, -0.005741244255806215 ], [ -0.005741244255806215, 0.9398093474585438 ] ], "crowding_model_dimension": 2, "feature_scale_nominal": 1.0, "feature_scale_pre_crowding": 0.9632340578177712, "feature_scale_post_crowding_median_edge": 0.9390964734443098, "pre_crowding_edge_length_summary": { "min": 0.9237865569090764, "median": 0.9632340578177712, "mean": 0.9741314104281011, "max": 1.0782024743327696 }, "post_crowding_edge_length_summary": { "min": 0.888274450836998, "median": 0.9390964734443098, "mean": 0.9475442060583654, "max": 1.0531799899889709 }, "pre_crowding_min_nonadjacent_node_distance": 2.5149595929643613, "pre_crowding_min_nonincident_edge_distance": Infinity, "pre_crowding_min_nonincident_node_edge_distance": 2.6770901339659394, "crowding_gamma_min_search_tolerance": 0.005, "crowding_gamma_min_search_history": [ { "gamma": 0.01, "admissible": false, "realized_separation_ratio": 0.0798040918777844 }, { "gamma": 1.0, "admissible": true, "realized_separation_ratio": 2.610953768248249 }, { "gamma": 0.505, "admissible": true, "realized_separation_ratio": 1.3201374191051922 }, { "gamma": 0.2575, "admissible": true, "realized_separation_ratio": 0.6762583947022294 }, { "gamma": 0.13375, "admissible": true, "realized_separation_ratio": 0.35712318819124134 }, { "gamma": 0.07187500000000001, "admissible": false, "realized_separation_ratio": 0.20217643659046214 }, { "gamma": 0.1028125, "admissible": false, "realized_separation_ratio": 0.2787234495484941 }, { "gamma": 0.11828125, "admissible": true, "realized_separation_ratio": 0.3177766847741673 }, { "gamma": 0.110546875, "admissible": true, "realized_separation_ratio": 0.2982061872172346 }, { "gamma": 0.10667968750000001, "admissible": true, "realized_separation_ratio": 0.2884527351158281 } ], "crowding_gamma_min_search_iterations": 10, "crowding_gamma_min_search_bracket": [ 0.1028125, 0.10667968750000001 ], "crowding_relative_budget_definition": "gamma = 1 - r * (1 - gamma_min)", "requested_noise_ratio": 0.04285250616657629, "realized_noise_ratio": 0.04285250616657629, "max_admissible_noise_ratio_after_crowding": 0.34792455831639857, "requested_crowding_r": 0.06799159982269508, "realized_crowding_r": 0.06799159982269508, "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling", "tube_no_overlap_required_centerline_clearance": 0.4461995161851111, "tube_no_overlap_post_crowding_margin": 1.9161373252320861, "tube_no_overlap_satisfied": true, "tube_no_overlap_constraint_active": true, "max_admissible_tube_radius_after_crowding": 1.085463408375446, "realized_tube_radius_budget_fraction": 0.1173643853642821, "point_cloud_params": { "feature_scale": 1.0, "sampling_density_per_feature": 24.593173564220816, "noise_ratio": 0.04285250616657629, "sigma": 0.04285250616657629, "embedding_dimension": 2, "include_node_points": true, "include_junction_points": true, "node_tube_sampling_policy": "edge_tubes_only_except_isolated_nodes", "min_points_per_edge": 2, "density_jitter_ratio_range": [ 0.0, 0.15 ], "endpoint_sampling_mode": "include", "feature_thickness_ratio": 0.12739474575940296, "feature_thickness_radius": 0.12739474575940296, "tube_sampling_mode": "solid" }, "num_clean_points": 254, "num_edge_sampled_points": 244, "num_node_sampled_points": 10, "point_component_id": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], "component_point_ids": [ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253 ] ], "nearest_feature_changed_rate": 0.0984251968503937, "nonincident_feature_confusion_rate": 0.08267716535433071, "cross_component_confusion_rate": 0.0, "noise_overlap_quality_pass": true, "noise_overlap_quality_thresholds": { "nonincident_feature_confusion_rate": 0.12, "cross_component_confusion_rate": 0.03 }, "num_points_evaluated_for_noise_confusion": 254, "num_nearest_feature_changes": 25, "num_nonincident_feature_confusions": 21, "num_cross_component_confusions": 0, "sample_id": 47, "difficulty": "full", "difficulty_coordinate": { "noise_ratio": 0.04285250616657629, "crowding_r": 0.06799159982269508, "sampling_density_per_feature": 24.593173564220816, "feature_thickness_ratio": 0.782242435794394, "num_components": 1, "requested_embedding_dimension": 2 }, "realized_geometry": { "realized_separation_to_feature_scale": 2.3623368414171972, "realized_absolute_hardness": 0.42330965782173835, "crowding_gamma": 0.9392617227990151, "crowding_gamma_min": 0.10667968750000001, "feature_thickness_radius": 0.12739474575940296, "feature_thickness_budget": 0.782242435794394, "effective_max_tube_radius_for_sampling": 0.16285839265422775, "max_admissible_tube_radius_before_crowding": 0.16285839265422775, "cycle_hole_radius_cap": 0.16285839265422775, "cycle_hole_radius_fraction": 0.2, "requested_noise_ratio": 0.04285250616657629, "realized_noise_ratio": 0.04285250616657629, "max_admissible_noise_ratio_after_crowding": 0.34792455831639857, "requested_crowding_r": 0.06799159982269508, "realized_crowding_r": 0.06799159982269508, "thickness_aware_min_required_clearance": 0.27478949151880594, "thickness_clearance_noise_margin": 0.17141002466630517, "minimum_realized_component_gap": Infinity }, "graph_summary": { "num_nodes": 10, "num_edges": 10, "num_components": 1, "num_clean_points": 254, "topology_classes": [ "single_cycle" ] }, "seed_bundle": { "point_cloud_seed": 350320930, "component_seed_bundles": [ { "topology_seed": 686470320, "branch_seed": 846440009, "embedding_seed": 41251067, "topology_class": "single_cycle" } ] }, "scheduled_normalized_axes": { "noise_ratio": 0.12695836759209053, "crowding_r": 0.11331933303782513, "sampling_density_per_feature": 0.018922159803683107, "feature_thickness_ratio": 0.6040771559898073 }, "scheduled_vector_magnitude": 0.31393747660249005, "scheduled_sample_rank": 47, "actual_normalized_axes": { "noise_ratio": 0.12695836759209053, "crowding_r": 0.11331933303782513, "sampling_density_per_feature": 0.018922159803683107, "feature_thickness_ratio": 0.6040771559898073 }, "actual_difficulty_coordinate": [ 0.04285250616657629, 0.06799159982269508, 24.593173564220816, 0.782242435794394 ], "difficulty_relaxation_factor": 1.0 }